{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "1498fc1e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-10\n",
      "-8.0\n",
      "-6.4\n",
      "-5.12\n",
      "-4.096\n",
      "-3.2768\n",
      "-2.62144\n",
      "-2.0971520000000003\n",
      "-1.6777216000000004\n",
      "-1.3421772800000003\n",
      "-1.0737418240000003\n",
      "-0.8589934592000003\n",
      "-0.6871947673600002\n",
      "-0.5497558138880001\n",
      "-0.43980465111040007\n",
      "-0.35184372088832006\n",
      "-0.281474976710656\n",
      "-0.22517998136852482\n",
      "-0.18014398509481985\n",
      "-0.14411518807585588\n",
      "-0.11529215046068471\n",
      "-0.09223372036854777\n",
      "-0.07378697629483821\n",
      "-0.05902958103587057\n",
      "-0.04722366482869646\n",
      "-0.037778931862957166\n",
      "-0.030223145490365734\n",
      "-0.024178516392292588\n",
      "-0.01934281311383407\n",
      "-0.015474250491067256\n",
      "-0.012379400392853806\n",
      "-0.009903520314283045\n",
      "-0.007922816251426436\n",
      "-0.006338253001141149\n",
      "-0.00507060240091292\n",
      "-0.0040564819207303355\n",
      "-0.0032451855365842686\n",
      "-0.002596148429267415\n",
      "-0.002076918743413932\n",
      "-0.0016615349947311456\n",
      "-0.0013292279957849164\n",
      "-0.001063382396627933\n",
      "-0.0008507059173023465\n",
      "-0.0006805647338418772\n",
      "-0.0005444517870735017\n",
      "-0.0004355614296588014\n",
      "-0.0003484491437270411\n",
      "-0.00027875931498163285\n",
      "-0.00022300745198530628\n",
      "-0.00017840596158824503\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 加载依赖库\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# 定义 y=x^2+1 函数\n",
    "def function(x):\n",
    "    y = x ** 2 + 1\n",
    "    return y\n",
    "\n",
    "# 指定自变量更新迭代次数（迭代的次数）\n",
    "epoch = 50\n",
    "# 指定学习率\n",
    "lr = 0.1\n",
    "# 初始化变量\n",
    "xi = -10\n",
    "\n",
    "# 求函数梯度\n",
    "def get_gradient(x):\n",
    "    gradient = 2 * x\n",
    "    return gradient\n",
    "\n",
    "# 储存更新后的梯度值\n",
    "trajectory = []\n",
    "\n",
    "# 利用梯度下降算法找到使函数取得最小值的自变量的值x_star\n",
    "def get_x_star(xi):\n",
    "    for i in range(epoch):\n",
    "        trajectory.append(xi)\n",
    "        print(xi)\n",
    "        xi = xi - lr * get_gradient(xi)\n",
    "    x_star = xi\n",
    "    return x_star\n",
    "\n",
    "get_x_star(xi)\n",
    "# print(trajectory)\n",
    "\n",
    "x = np.arange(-10, 10, 0.1)\n",
    "y = function(x)\n",
    "\n",
    "# 画出函数图像\n",
    "plt.plot(x, y)\n",
    "x_trajectory = np.array(trajectory)\n",
    "y_trajectory = function(x_trajectory)\n",
    "\n",
    "# Scatter plot for the trajectory\n",
    "plt.scatter(x_trajectory, y_trajectory, color='red', label='Gradient Descent Steps')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.title('Gradient Descent on $f(x) = x^2 + 1$')\n",
    "plt.legend()\n",
    "plt.grid()\n",
    "plt.show()\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "# if __name__ == '__main__':\n",
    "#     epoch = 50\n",
    "#     lr = 0.1\n",
    "#     xi = -18\n",
    "\n",
    "#     trajectory = []\n",
    "\n",
    "#     for i in range(epoch):\n",
    "#         trajectory.append(xi)\n",
    "#         print(xi)\n",
    "#         xi = xi - lr * function()\n",
    "\n",
    "#     x = np.arange(-20, 20, 0.1)\n",
    "#     y = x ** 2 + 1\n",
    "\n",
    "#     # 画出函数图像\n",
    "#     plt.plot(x, y)\n",
    "#     x_trajectory = np.array(trajectory)\n",
    "#     y_trajectory = x_trajectory ** 2 + 1\n",
    "\n",
    "#     plt.scatter(x_trajectory, y_trajectory, color=\"red\", label='Gradient Descent Steps')\n",
    "#     plt.title('Gradient Descent on $f(x) = x^2 + 1$')\n",
    "#     plt.xlabel(\"x\")\n",
    "#     plt.ylabel('y')\n",
    "#     # tap标签\n",
    "#     plt.legend()\n",
    "#     # grid 网格背景\n",
    "#     plt.grid()\n",
    "#     plt.show()\n",
    "\n",
    "# import torch\n",
    "\n",
    "# print(torch.arange(12))\n",
    "\n",
    "\n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "base",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
